Trigonometry Small Angles Limit - 2

The second does not come from the first, it comes from the BUT....

\(sin\frac{\theta}{2}<\frac{\theta}{2}\\ \qquad \text{remember that theta is describes as acute so therefore it is positive}\\ sin^2\frac{\theta}{2}<\left(\frac{\theta}{2}\right)^2\\ -sin^2\frac{\theta}{2}>-\left(\frac{\theta}{2}\right)^2\\ 1-sin^2\frac{\theta}{2}>1-\left(\frac{\theta}{2}\right)^2\\\)

Thanks Melody for your patience and skills!